Now, the frequency dependent response coefficient χ(ω) -- or the response function -- is defined as the ratio m(ω)/h(ω). Note that the response function takes complex values to allow for the possibility of a phase lag between the output and the input. The 90-degree-out-of-phase component of the response is directly relate to the amount of dissipation of energy that will result from the response.

Now that we have the response function we can calculate the time-varying response to any time-varying generalize stress by the principle of superposition. Fourier tells us that we can write any time-varying function, h(t), as a superposition of harmonic functions:

h(t) = +∞ ∫-∞ h(ω) dω

And by the principle of superposition, the response will be a superposition of the corresponding responses: